Recovering piecewise constant refractive indices by a single far-field pattern

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journal

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Original languageEnglish
Article number085005
Journal / PublicationInverse Problems
Issue number8
Online published20 Aug 2020
Publication statusPublished - Aug 2020


We are concerned with the inverse scattering problem of recovering an inhomogeneous medium by the associated acoustic wave measurement. We prove that under certain assumptions, a single far-field pattern determines the values of a perturbation to the refractive index on the corners of its support. These assumptions are satisfied for example in the low acoustic frequency regime. As a consequence if the perturbation is piecewise constant with either a polyhedral nest geometry or a known polyhedral cell geometry, such as a pixel or voxel array, we establish the injectivity of the perturbation to far-field map given a fixed incident wave. This is the first unique determinancy result of its type in the literature, and all of the existing results essentially make use of infinitely many measurements.

Research Area(s)

  • inverse medium scattering, uniqueness, single far-field pattern, value at corner, piecewise constant, polyhedral